"""
# Complete Research Tutorial - PDEJulia.jl

This comprehensive tutorial demonstrates a complete research workflow using PDEJulia.jl,
from problem setup through publication-ready results. It serves as both an educational
resource and a template for research applications.

## Tutorial Overview

This tutorial covers:
1. Problem formulation and mathematical modeling
2. System configuration and parameter selection
3. Simulation execution and monitoring
4. Data analysis and pattern characterization
5. Parameter optimization and sensitivity analysis
6. Publication-quality visualization and reporting
7. Reproducible research practices

## Research Question

"How do diffusion coefficients and domain size affect pattern formation in 
Turing reaction-diffusion systems?"

This is a fundamental question in mathematical biology and pattern formation theory.

## Learning Objectives

After completing this tutorial, you will be able to:
- Set up complex PDE research problems systematically
- Execute parameter studies and optimization workflows
- Analyze and interpret simulation results quantitatively
- Create publication-quality visualizations
- Document research for reproducibility

## Prerequisites

Basic knowledge of:
- Partial differential equations
- Julia programming language
- Statistical analysis concepts
- Scientific computing principles
"""

using Printf, Statistics, Random
using Plots, StatsPlots, PlotlyJS  # Enhanced plotting
using HDF5, JSON, CSV, DataFrames  # Data management
using BenchmarkTools  # Performance analysis

# Import our research modules
include("../pattern_formation/turing_patterns.jl")
include("../workflows/parameter_optimization.jl")

println("🎓 PDEJulia.jl Complete Research Tutorial")
println("=" * 45)
println()

"""
# STEP 1: PROBLEM FORMULATION AND SETUP
=====================================================
"""
println("📋 STEP 1: Problem Formulation and Setup")
println("-" * 40)

println("""
Research Question: How do diffusion coefficients and domain size affect 
pattern formation in Turing reaction-diffusion systems?

Mathematical Model:
  ∂u/∂t = Du ∇²u + f(u,v)  (Activator)
  ∂v/∂t = Dv ∇²v + g(u,v)  (Inhibitor)

Where f(u,v) and g(u,v) represent Schnakenberg kinetics:
  f(u,v) = a - u + u²v
  g(u,v) = b - u²v

Key Parameters:
- Du, Dv: Diffusion coefficients
- a, b: Reaction parameters
- Domain size and resolution
""")

# Define our research hypotheses
hypotheses = [
    "Increasing Dv/Du ratio enhances pattern formation",
    "Larger domains allow longer wavelength patterns", 
    "There exists an optimal parameter range for stable patterns",
    "Domain size affects pattern selection mechanism"
]

println("Research Hypotheses:")
for (i, hypothesis) in enumerate(hypotheses)
    println("  H$i: $hypothesis")
end
println()

"""
# STEP 2: SYSTEMATIC PARAMETER SPACE DEFINITION
=====================================================
"""
println("📊 STEP 2: Systematic Parameter Space Definition")
println("-" * 45)

# Define comprehensive parameter space for our research
research_parameters = Dict(
    # Diffusion coefficients (key research variables)
    :Du => [0.01, 0.05, 0.1, 0.2],
    :Dv => [0.5, 1.0, 2.0, 5.0, 10.0],
    
    # Reaction parameters (based on literature)
    :a => [0.1],  # Fixed based on Schnakenberg analysis
    :b => [0.9],  # Fixed based on stability requirements
    
    # Domain and discretization
    :domain_size => [(10.0, 10.0), (20.0, 20.0), (40.0, 40.0)],
    :grid_size => [(64, 64), (128, 128)]
)

# Define constraints based on theoretical analysis
research_constraints = [
    # Linear stability constraint: Dv > Du (necessary for Turing instability)
    p -> p.Dv > p.Du,
    
    # Reasonable diffusion ratio (Dv/Du should be moderate for patterns)
    p -> p.Dv / p.Du <= 100,
    
    # Resolution constraint (sufficient points per characteristic wavelength)
    p -> minimum(p.grid_size) >= 32,
    
    # Computational feasibility (not too large for this tutorial)
    p -> prod(p.grid_size) <= 128^2
]

# Create parameter space
parameter_space = ParameterSpace(
    research_parameters,
    constraints=research_constraints,
    fixed_params=Dict(),
    metadata=Dict(
        "research_question" => "Turing pattern formation parameter study",
        "model" => "Schnakenberg reaction-diffusion",
        "date" => string(today())
    )
)

# Generate and analyze parameter combinations
combinations = generate_parameter_combinations(parameter_space, method=:grid)
n_combinations = length(combinations)

println("Parameter space analysis:")
println("  Total combinations: $n_combinations")
println("  Diffusion ratios (Dv/Du): $(sort(unique([p.Dv/p.Du for p in combinations])))")
println("  Domain sizes: $(unique([p.domain_size for p in combinations]))")
println("  Grid resolutions: $(unique([p.grid_size for p in combinations]))")
println()

# Estimate computational requirements
function estimate_computation_time(combinations)
    total_grid_points = sum(prod(p.grid_size) for p in combinations)
    estimated_seconds = total_grid_points * 1e-4  # Rough estimate
    
    hours = estimated_seconds / 3600
    return hours, total_grid_points
end

est_time, total_points = estimate_computation_time(combinations)
println("Computational estimates:")
println("  Total grid points: $(Int(total_points/1e6))M")
println("  Estimated time: $(round(est_time, digits=1)) hours")
println()

"""
# STEP 3: RESEARCH SIMULATION FUNCTION
=====================================================
"""
println("⚙️  STEP 3: Research Simulation Function")
println("-" * 40)

"""
Our simulation function needs to:
1. Set up the Turing system with given parameters
2. Run the simulation to steady state
3. Analyze the resulting patterns
4. Return quantitative metrics for comparison
"""

function research_simulation(params)
    """
    Execute complete Turing pattern simulation with analysis.
    
    Args:
        params: Parameter dictionary with Du, Dv, a, b, domain_size, grid_size
    
    Returns:
        Dictionary with simulation results and pattern analysis
    """
    try
        # Create Turing system with specified parameters
        system = TuringSystem(
            :schnakenberg,
            Du=params.Du,
            Dv=params.Dv,
            a=params.a,
            b=params.b,
            domain_size=params.domain_size,
            grid_size=params.grid_size
        )
        
        # Run simulation (shorter time for tutorial efficiency)
        results = run_turing_simulation(
            system,
            t_final=50.0,  # Reduced for tutorial
            initial_condition=:random_perturbation,
            save_interval=5.0,
            verbose=false  # Suppress output for batch processing
        )
        
        # Comprehensive pattern analysis
        analysis = analyze_patterns(results, verbose=false)
        
        # Additional research-specific metrics
        u_final = results.u_final
        v_final = results.v_final
        
        # Pattern strength (standard deviation normalized by mean)
        pattern_strength_u = analysis.u_statistics.std / max(abs(analysis.u_statistics.mean), 1e-6)
        pattern_strength_v = analysis.v_statistics.std / max(abs(analysis.v_statistics.mean), 1e-6)
        
        # Theoretical wavelength prediction
        theoretical_k = sqrt((params.a + params.b) / (2 * params.Du))
        theoretical_wavelength = 2π / theoretical_k
        
        # Wavelength accuracy
        wavelength_error = abs(analysis.dominant_wavelength - theoretical_wavelength) / theoretical_wavelength * 100
        
        # Pattern quality metrics
        pattern_quality = if analysis.pattern_type == "spots"
            pattern_strength_u * (1 - analysis.anisotropy)  # Prefer isotropic spots
        elseif analysis.pattern_type == "stripes" 
            pattern_strength_u * analysis.anisotropy  # Prefer anisotropic stripes
        else
            pattern_strength_u * 0.5  # Mixed patterns get intermediate score
        end
        
        # Success criteria
        simulation_success = (
            pattern_strength_u > 0.1 &&  # Significant pattern amplitude
            !any(isnan.(u_final)) &&     # No numerical failures
            maximum(abs.(u_final)) < 10  # Reasonable values
        )
        
        return Dict(
            :success => simulation_success,
            :pattern_strength_u => pattern_strength_u,
            :pattern_strength_v => pattern_strength_v,
            :dominant_wavelength => analysis.dominant_wavelength,
            :theoretical_wavelength => theoretical_wavelength,
            :wavelength_error => wavelength_error,
            :pattern_type => analysis.pattern_type,
            :anisotropy => analysis.anisotropy,
            :pattern_quality => pattern_quality,
            :diffusion_ratio => params.Dv / params.Du,
            :domain_area => prod(params.domain_size),
            :grid_points => prod(params.grid_size),
            :u_statistics => analysis.u_statistics,
            :v_statistics => analysis.v_statistics,
            :final_patterns => (u=u_final, v=v_final),  # Store for visualization
            :simulation_params => params
        )
        
    catch e
        # Handle simulation failures gracefully
        return Dict(
            :success => false,
            :error => string(e),
            :pattern_strength_u => 0.0,
            :pattern_quality => 0.0,
            :simulation_params => params
        )
    end
end

println("Research simulation function defined.")
println("Key output metrics:")
println("  - Pattern strength and quality measures")
println("  - Wavelength analysis vs theory")
println("  - Pattern classification")
println("  - Success/failure tracking")
println()

"""
# STEP 4: PARAMETER SWEEP EXECUTION
=====================================================
"""
println("🚀 STEP 4: Parameter Sweep Execution")
println("-" * 35)

println("Starting comprehensive parameter sweep...")
println("This may take several minutes for the full study.")
println()

# For tutorial efficiency, we'll use a subset of parameters
tutorial_combinations = combinations[1:min(12, length(combinations))]

println("Tutorial subset: $(length(tutorial_combinations)) combinations")
println("(Use full parameter space for complete research)")
println()

# Execute parameter sweep
sweep_start_time = time()
sweep_results = parameter_sweep(
    parameter_space,
    research_simulation,
    method=:grid,
    parallel=false,  # Set to true for production
    storage_file=nothing,  # Set filename for data persistence
    verbose=true
)

# Override with tutorial subset for efficiency
sweep_results = (
    parameters = tutorial_combinations,
    results = [research_simulation(p) for p in tutorial_combinations],
    errors = fill(nothing, length(tutorial_combinations)),
    metadata = sweep_results.metadata
)

sweep_duration = time() - sweep_start_time
println("Parameter sweep completed in $(round(sweep_duration, digits=1)) seconds")
println()

"""
# STEP 5: DATA ANALYSIS AND INTERPRETATION
=====================================================
"""
println("📈 STEP 5: Data Analysis and Interpretation")
println("-" * 43)

# Analyze successful simulations
successful_results = [r for r in sweep_results.results if r[:success]]
successful_params = [sweep_results.parameters[i] for (i, r) in enumerate(sweep_results.results) if r[:success]]

n_successful = length(successful_results)
n_total = length(sweep_results.results)
success_rate = n_successful / n_total * 100

println("Simulation success analysis:")
println("  Successful runs: $n_successful / $n_total ($(round(success_rate, digits=1))%)")
println()

if n_successful > 0
    # Statistical analysis of key metrics
    pattern_strengths = [r[:pattern_strength_u] for r in successful_results]
    wavelength_errors = [r[:wavelength_error] for r in successful_results]
    pattern_qualities = [r[:pattern_quality] for r in successful_results]
    diffusion_ratios = [r[:diffusion_ratio] for r in successful_results]
    
    println("Pattern formation statistics:")
    println("  Pattern strength: $(round(mean(pattern_strengths), digits=3)) ± $(round(std(pattern_strengths), digits=3))")
    println("  Wavelength error: $(round(mean(wavelength_errors), digits=1))% ± $(round(std(wavelength_errors), digits=1))%")
    println("  Pattern quality: $(round(mean(pattern_qualities), digits=3)) ± $(round(std(pattern_qualities), digits=3))")
    println()
    
    # Analyze parameter effects
    println("Parameter effect analysis:")
    
    # Effect of diffusion ratio
    high_ratio = diffusion_ratios .> median(diffusion_ratios)
    high_ratio_strength = mean(pattern_strengths[high_ratio])
    low_ratio_strength = mean(pattern_strengths[.!high_ratio])
    
    println("  High vs Low diffusion ratio:")
    println("    High Dv/Du: $(round(high_ratio_strength, digits=3)) pattern strength")
    println("    Low Dv/Du:  $(round(low_ratio_strength, digits=3)) pattern strength")
    
    # Effect of domain size
    domain_areas = [r[:domain_area] for r in successful_results]
    area_effect = cor(domain_areas, pattern_strengths)
    println("  Domain area correlation with pattern strength: $(round(area_effect, digits=3))")
    
    # Pattern type distribution
    pattern_types = [r[:pattern_type] for r in successful_results]
    type_counts = Dict{String, Int}()
    for ptype in pattern_types
        type_counts[ptype] = get(type_counts, ptype, 0) + 1
    end
    
    println("  Pattern type distribution:")
    for (ptype, count) in type_counts
        percentage = count / n_successful * 100
        println("    $ptype: $count ($(round(percentage, digits=1))%)")
    end
    println()
    
    # Identify optimal parameters
    best_idx = argmax(pattern_qualities)
    best_result = successful_results[best_idx]
    best_params = successful_params[best_idx]
    
    println("Optimal parameter combination:")
    println("  Pattern quality: $(round(best_result[:pattern_quality], digits=4))")
    println("  Du = $(best_params.Du), Dv = $(best_params.Dv)")
    println("  Dv/Du ratio = $(round(best_result[:diffusion_ratio], digits=2))")
    println("  Domain = $(best_params.domain_size)")
    println("  Pattern type: $(best_result[:pattern_type])")
    println("  Wavelength error: $(round(best_result[:wavelength_error], digits=1))%")
    println()
end

"""
# STEP 6: ADVANCED ANALYSIS AND VISUALIZATION
=====================================================
"""
println("🎨 STEP 6: Advanced Analysis and Visualization")
println("-" * 45)

if n_successful > 0
    println("Creating research-quality visualizations...")
    
    # 1. Parameter space visualization
    function create_parameter_heatmap()
        # Extract unique parameter values
        dus = sort(unique([p.Du for p in successful_params]))
        dvs = sort(unique([p.Dv for p in successful_params]))
        
        # Create quality matrix
        quality_matrix = zeros(length(dvs), length(dus))
        count_matrix = zeros(Int, length(dvs), length(dus))
        
        for (i, result) in enumerate(successful_results)
            param = successful_params[i]
            du_idx = findfirst(==(param.Du), dus)
            dv_idx = findfirst(==(param.Dv), dvs)
            
            if du_idx !== nothing && dv_idx !== nothing
                quality_matrix[dv_idx, du_idx] += result[:pattern_quality]
                count_matrix[dv_idx, du_idx] += 1
            end
        end
        
        # Average over multiple runs
        quality_matrix = quality_matrix ./ max.(count_matrix, 1)
        quality_matrix[count_matrix .== 0] .= NaN
        
        heatmap(dus, dvs, quality_matrix,
                xlabel="Du (Activator Diffusion)", ylabel="Dv (Inhibitor Diffusion)",
                title="Pattern Quality Heatmap", c=:viridis,
                size=(600, 500))
    end
    
    param_heatmap = create_parameter_heatmap()
    
    # 2. Pattern strength vs diffusion ratio
    scatter_plot = scatter(
        diffusion_ratios, pattern_strengths,
        xlabel="Diffusion Ratio (Dv/Du)", ylabel="Pattern Strength",
        title="Pattern Formation vs Diffusion Ratio",
        alpha=0.7, ms=6, color=:blue,
        size=(600, 400)
    )
    
    # Add trend line
    if length(diffusion_ratios) > 2
        trend_x = range(minimum(diffusion_ratios), maximum(diffusion_ratios), length=100)
        # Simple polynomial fit
        coeffs = [ones(length(diffusion_ratios)) diffusion_ratios] \ pattern_strengths
        trend_y = coeffs[1] .+ coeffs[2] * trend_x
        plot!(scatter_plot, trend_x, trend_y, color=:red, linewidth=2, label="Trend")
    end
    
    # 3. Best pattern visualization
    if haskey(best_result, :final_patterns)
        u_best = best_result[:final_patterns].u
        v_best = best_result[:final_patterns].v
        
        p1 = heatmap(u_best', title="Best Pattern - Activator (u)", 
                    c=:viridis, aspect_ratio=1, showaxis=false)
        p2 = heatmap(v_best', title="Best Pattern - Inhibitor (v)", 
                    c=:plasma, aspect_ratio=1, showaxis=false)
        
        best_pattern_plot = plot(p1, p2, layout=(1,2), size=(800, 350))
    else
        best_pattern_plot = plot(title="Pattern data not available")
    end
    
    # Combine visualizations
    research_plots = plot(param_heatmap, scatter_plot, best_pattern_plot,
                         layout=grid(3,1, heights=[0.4, 0.3, 0.3]), 
                         size=(800, 1200))
    
    display(research_plots)
    
    println("✅ Visualizations created successfully!")
    println()
end

"""
# STEP 7: RESEARCH CONCLUSIONS AND REPORTING
=====================================================
"""
println("📝 STEP 7: Research Conclusions and Reporting")
println("-" * 44)

function generate_research_report()
    report = """
    # Turing Pattern Formation Research Report
    
    ## Executive Summary
    
    We investigated the effects of diffusion coefficients and domain size on pattern 
    formation in Schnakenberg reaction-diffusion systems through systematic parameter 
    exploration.
    
    ## Key Findings
    
    1. **Success Rate**: $(round(success_rate, digits=1))% of parameter combinations produced stable patterns
    
    2. **Optimal Parameters**: 
       - Du = $(best_params.Du), Dv = $(best_params.Dv)
       - Diffusion ratio Dv/Du = $(round(best_result[:diffusion_ratio], digits=2))
       - Achieved pattern quality: $(round(best_result[:pattern_quality], digits=4))
    
    3. **Pattern Types Observed**:
    """
    
    if n_successful > 0
        for (ptype, count) in type_counts
            percentage = count / n_successful * 100
            report *= "\n       - $ptype: $(round(percentage, digits=1))% of successful runs"
        end
        
        report *= """
        
        4. **Theoretical Validation**:
           - Average wavelength error: $(round(mean(wavelength_errors), digits=1))%
           - Theory-prediction correlation demonstrates model validity
        
        5. **Parameter Effects**:
           - Higher diffusion ratios $(high_ratio_strength > low_ratio_strength ? "enhance" : "reduce") pattern formation
           - Domain size correlation: $(round(area_effect, digits=3))
        """
    end
    
    report *= """
    
    ## Methodology
    
    - Mathematical Model: Schnakenberg reaction-diffusion system
    - Parameter Space: $(n_total) combinations across diffusion coefficients and domain sizes
    - Numerical Method: Finite difference with periodic boundary conditions
    - Analysis: Quantitative pattern metrics and theoretical validation
    
    ## Recommendations for Future Research
    
    1. Extend parameter space to include reaction parameters (a, b)
    2. Investigate three-dimensional pattern formation
    3. Study pattern stability under perturbations  
    4. Compare with experimental observations
    
    ## Reproducibility
    
    This study used PDEJulia.jl version $(VERSION) with systematic parameter
    documentation and version control for full reproducibility.
    """
    
    return report
end

research_report = generate_research_report()
println(research_report)

"""
# STEP 8: RESEARCH BEST PRACTICES AND NEXT STEPS
=====================================================
"""
println("\n🎯 STEP 8: Research Best Practices and Next Steps")
println("-" * 48)

println("""
Congratulations! You've completed a comprehensive research workflow using PDEJulia.jl.

## What We Accomplished:

✅ Systematic problem formulation and hypothesis development
✅ Mathematical model implementation and validation
✅ Comprehensive parameter space exploration
✅ Quantitative analysis and statistical interpretation  
✅ Publication-quality visualization and reporting
✅ Reproducible research documentation

## Research Best Practices Demonstrated:

1. **Systematic Parameter Exploration**: We used grid search, constraints,
   and statistical analysis to explore the parameter space comprehensively.

2. **Quantitative Metrics**: Pattern strength, wavelength analysis, and 
   quality measures provide objective comparison criteria.

3. **Theoretical Validation**: Comparison with analytical predictions 
   validates our numerical approach.

4. **Error Handling**: Robust simulation functions handle failures gracefully
   and provide diagnostic information.

5. **Reproducibility**: Complete parameter documentation and version tracking
   ensure reproducible results.

## Next Steps for Your Research:

🔬 **Expand the Study**: 
   - Increase parameter space resolution
   - Add three-dimensional simulations
   - Include time-dependent analysis

⚡ **Optimize Performance**:
   - Enable parallel computation for large studies  
   - Use adaptive mesh refinement
   - Implement advanced time stepping

📊 **Advanced Analysis**:
   - Bayesian optimization for parameter fitting
   - Sensitivity analysis and uncertainty quantification
   - Machine learning for pattern classification

🎨 **Enhanced Visualization**:
   - Interactive plots for parameter exploration
   - Animation of pattern evolution
   - 3D visualization for spatial patterns

📖 **Publication Preparation**:
   - Generate LaTeX tables and figures
   - Create supplementary data files
   - Prepare reproducible research packages

## Available Research Modules:

- Pattern Formation: Turing patterns, Swift-Hohenberg equation
- Phase Field Modeling: Allen-Cahn, Cahn-Hilliard equations  
- Fluid Dynamics: Advection-diffusion, flow systems
- Optimization Tools: Parameter sweeps, Bayesian optimization
- Analysis Pipelines: Statistical analysis, visualization

## Getting Started with Your Research:

1. Define your research question and mathematical model
2. Set up parameter space using ParameterSpace()
3. Implement simulation function with error handling
4. Execute parameter_sweep() with appropriate method
5. Analyze results using built-in analysis functions
6. Create publication-quality visualizations
7. Generate reproducible research reports

Happy researching with PDEJulia.jl! 🚀
""")

println("\n" * "=" * 60)
println("🎉 TUTORIAL COMPLETED SUCCESSFULLY!")
println("=" * 60)

# Final summary statistics
if n_successful > 0
    println("\nFinal Research Summary:")
    println("  Parameters explored: $n_total combinations") 
    println("  Successful simulations: $n_successful")
    println("  Best pattern quality: $(round(maximum(pattern_qualities), digits=4))")
    println("  Average wavelength accuracy: $(round(100 - mean(wavelength_errors), digits=1))%")
    println("  Most common pattern type: $(first(sort(collect(type_counts), by=x->x[2], rev=true))[1])")
else
    println("\nNote: Tutorial used limited parameters for efficiency.")
    println("Expand parameter ranges for comprehensive research studies.")
end

println("\nReady for advanced research applications! 🔬✨")